Massive Massive Multiple-input Multiple-output Downlink Research Articles

Massive MIMO uplink and downlink joint representation based on couple dictionary learning

AbstractThe challenge of jointly representing both the uplink (UL) and downlink (DL) in massive multiple input multiple output (MIMO) systems have been tackled. Considering the angular reciprocity, a couple dictionary learning (CDL) support to enhance performance and address high complexity has been introduced. This approach minimizes the number of pilots and improves accuracy. Currently, accuracy analysis of UL/DL representation primarily relies on simulation. To bridge this gap, a proportion factor (PF) operator is proposed for CDL to assess accuracy. Specifically, a qualitative analysis formula is provided for accuracy and an optimal upper bound is established. Through theoretical proof, it is demonstrated that the accuracy of CDL for representation is mainly influenced by the cross‐correlation between the pilot matrix and the dictionary matrix. Inspired by PF operator, an optimal couple dictionary learning (OCDL) algorithm using singular value decomposition (SVD) is introduced to obtain dictionary updating, aiming at high‐precision representation. By establishing normalized mean squared error (NMSE), successful representation ratio, bit error rate (BER), and constellation performance, an OCDL algorithm that outperforms existing methods is showcased and channel representation accuracy is enhanced significantly.

Power allocation optimization for hybrid information and energy transfer with massive MIMO downlink

AbstractThis paper investigates the power allocation in a massive multiple‐input multiple‐output (MIMO) downlink system, where the base station (BS) simultaneously transmits information and energy to information terminals and energy terminals without resorting to any wireless energy harvesting (EH) protocol, respectively. First, with respect to this system, the closed‐form expressions of achievable rate and harvested energy are, respectively, derived for Rayleigh fading channels. Then, from these expressions, three optimization problems are formulated based on quality‐of‐service (QoS) requirements, with the purposes of maximizing achievable sum rate, harvested sum energy and joint QoS requirements, respectively. The optimization problem of maximizing achievable sum rate is transformed into a sequence of geometric programmings (GPs), which can be solved efficiently with standard convex optimization tools. The optimization problem of maximizing harvested sum energy is proved to be solvable as a linear program. The optimization problem of maximizing joint QoS requirements is shown to be a multi‐objective optimization problem (MOOP) and solved by a one‐dimensional search based on GP. Finally, numerical results manifest that the proposed power allocation algorithms can provide good system performances of achievable sum rate and harvested sum energy, and jointly guarantee QoS fairness in terms of achievable rate and harvested energy.

Downlink Massive MIMO Systems: Reduction of Pilot Contamination for Channel Estimation with Perfect Knowledge of Large-Scale Fading

Massive multiple-input multiple-output (MIMO) technology is considered crucial for the development of future fifth-generation (5G) systems. However, a limitation of massive MIMO systems arises from the lack of orthogonality in the pilot sequences transmitted by users from a single cell to neighboring cells. To address this constraint, a proposed solution involves utilizing orthogonal pilot reuse sequences (PRS) and zero forced (ZF) pre-coding techniques. The primary objective of these techniques is to eradicate channel interference and improve the experience of end users who are afflicted by low-quality channels. The assessment of the channel involves evaluating its quality through channel assessment, conducting comprehensive evaluations of large-scale shutdowns, and analyzing the maximum transmission efficiency. By assigning PRS to a group of users, the proposed approach establishes lower bounds for the achievable downlink data rate (DR) and signal-to-interference noise ratio (SINR). These bounds are derived by considering the number of antennas approaches infinity which helps mitigate interference. Simulation results demonstrate that the utilization of improved channel evaluation and reduced loss leads to higher DR. When comparing different precoding techniques, the ZF method outperforms maximum ratio transmission (MRT) precoders in achieving a higher DR, particularly when the number of cells reaches 𝛶𝛶𝑝𝑝=7.

Evaluation of massive multiple-input multiple-output communication performance under a proposed improved minimum mean squared error precoding

<span lang="EN-US">The fundamental of a downlink massive multiple-input multiple-output (MIMO) energy- issue efficiency strategy is known as minimum mean squared error (MMSE) implementation degrades the performance of a downlink massive MIMO energy-efficiency scheme, so some improvements are adding for this precoding scheme to improve its workthat is called our proposal solution as a proposed improved MMSE precoder (PIMP). The energy efficiency (EE) study has also taken into mind drastically lowering radiated power while maintaining high throughput and minimizing interference issues. We further find the tradeoff between spectral efficiency (SE) and EE although they coincide at the beginning but later their interests become conflicting and divergent then leading EE to decrease so gradually while SE continues increasing logarithmically. The results achieved that for a single-cellular massive MU-MIMO downlink model, our PIMP scheme is the appropriate scenario to achieve higher precoding performance system. Furthermore, both maximum ratio transmission (MRT) and PIMP are suitable for performance improvement in massive MIMO results of EE and SE. So, the main contribution comes with this work that highest EE and SE are belong to use a PIMP which performs better appreciably than MRT at bigger ratio of number of antennas to the number of the users. </span>

Energy Efficiency Maximization Precoding for Quantized Massive MIMO Systems

The use of low-resolution digital-to-analog and analog-to-digital converters (DACs and ADCs) significantly benefits energy efficiency (EE) at the cost of high quantization noise for massive multiple-input multiple-output (MIMO) systems. This paper considers a precoding optimization problem for maximizing EE in quantized downlink massive MIMO systems. To this end, we jointly optimize an active antenna set, precoding vectors, and allocated power; yet acquiring such joint optimal solution is challenging. To resolve this challenge, we decompose the problem into precoding direction and power optimization problems. For precoding direction, we characterize the first-order optimality condition, which entails the effects of quantization distortion and antenna selection. We cast the derived condition as a functional eigenvalue problem, wherein finding the principal eigenvector attains the best local optimal point. To this end, we propose generalized power iteration based algorithm. To optimize precoding power for given precoding direction, we adopt a gradient descent algorithm for the EE maximization. Alternating these two methods, our algorithm identifies a joint solution of the active antenna set, the precoding direction, and allocated power. In simulations, the proposed methods provide considerable performance gains. Our results suggest that a few-bit DACs are sufficient for achieving high EE in massive MIMO systems.

Serving Mobile Users in Intelligent Reflecting Surface Assisted Massive MIMO System

As the number of antennas increases, the massive multiple-input multiple-output (MIMO) system can precisely point to user equipments (UEs) with narrow beams. Accurate and timely channel state information (CSI) feedback is crucial to keep UEs in service. Mobile UEs, however, may suffer from the narrow beam nature of the massive MIMO system since UEs can move out of the beam coverage. When intelligent reflecting surface (IRS) is applied to the massive MIMO system, the adjustment of the IRS cannot be frequent as the IRS is controlled remotely by the base station (BS). Limiting the number of CSI feedback and the number of both BS and IRS adjustments significantly reduces the overhead of transmission and computation to the system. In this paper, we consider the UEs’ mobility adaptation problem in an IRS assisted multiuser massive MIMO downlink system with infrequent CSI feedback. We propose a beam control method that adapts to UEs’ mobility. The problem is constructed as a sum rate problem where both the BS and IRS are taken into account to jointly optimize the beamforming matrices. Simulation results show that our proposed algorithm can converge quickly and provide satisfactory performance for mobile UEs. At the same time, our proposed algorithm reduces the frequency of updating the beamforming matrices effectively both at the BS and at the IRS.

Energy Efficiency Optimization Based on Power Allocation in Massive MIMO Downlink Systems

To solve the energy efficiency (EE) optimization in a multi-cell (MU) massive multiple-input multiple-output (MIMO) downlink system, of which channels are of symmetry in the Time-Division Duplex (TDD) protocol, we utilize a spatially correlated channel model and adopt the minimum mean-squared error (MMSE) estimator to tailor linear precoding vectors. Then, we derive the expression of downlink spectral efficiency (SE), taking interference into account. Subsequently, we establish the EE optimization function, which is defined as the average capacity divided by power consumption. In an interference-limited scenario, the EE optimization is of high complexity to solve globally as it is not jointly concave. To this end, we propose the Dinkelbach-like power allocation algorithm to obtain a suboptimal solution. We transform the EE problem in a fractional form into a subtractive optimization form called an auxiliary subproblem. Then, we relax the sub-problem to a concave problem by initializing the interference and omitting the dynamic power term about throughput. Lastly, we solve iteratively the Karush–Kuhn–Tucker (KKT) conditions by bisection search. Consequently, we obtain a sub-solution with modest complexity. The simulation results justify the rationality of the Dinkelbach-like algorithm and demonstrate that the proposal outperforms the reference schemes and effectively improves the performance metrics EE and SE.

Achievable Rate and Energy Efficiency Analysis of Multiuser Relay-Aided Massive MIMO Downlink

In this article, the achievable sum rate and the energy efficiency (EE) are investigated for a multiuser relay-aided massive multiple-input–multiple-output (MIMO) downlink. Low-resolution digital-to-analog converters (DACs) are equipped at both the base station (BS) and the relay station (RS), and the amplify-and-forward protocol is adopted at the RS. Under the Rician fading channel, closed-form approximate expressions for the achievable sum rate are derived with perfect and imperfect channel state information. A more general power law is extracted to save transmit power without reducing the achievable sum rate, and a local optimal power allocation scheme is proposed to improve the channel capacity of active users. Then, the tradeoff between the achievable sum rate and the EE is discussed. The numerical results show that, due to the quantization noise, the transmit power has a limited increase in the achievable rate. In addition, it is more valuable to improve the DAC quantization bit at the RS when the number of BS antennas is larger than that of RS antennas. In addition, under strong line-of-sight channels or high pilot transmit power conditions, the channel estimation accuracy is higher, and the best tradeoff between the achievable sum rate and the EE can be obtained when the DAC quantization bit is 4.

Sum Rate Analysis for Massive MIMO Downlink With MRC Beamforming and User Selection

Average allocation of data rate to each user is inefficient since the resource a base station can allocate is limited. Thus, user selection and user scheduling need to be applied into multi-user massive multiple-input multiple-output (MIMO) downlink system. In this paper, we mainly focus on the methods of user selection. First, we establish a downlink system model including transmission model and channel model. Then, two user-rate based user selection algorithms via the signal-to-interference-plus-noise-ratio (SINR) are proposed, where the SINR is generated by MRC beamforming. Finally, simulation results are provided to compare the performance of two proposed algorithms and their fairness towards selected users. In the simulation results, location-based selection algorithm and random selection algorithm are jointly compared. The second proposed algorithm possesses the highest total sum-rate and is the optimal algorithms among the four algorithms.

Utility Maximization for Large-Scale Cell-Free Massive MIMO Downlink

We consider utility maximization problems in the downlink cell-free massive multiple-input multiple-output (MIMO) whereby a large number of access points (APs) simultaneously serve a group of users. Four fundamental maximization objectives are of interest: (i) average spectral efficiency (SE), (ii) proportional fairness, (iii) harmonic-rate, and (iv) minimum SE of all users, subject to a sum power constraint at each AP. As considered problems are non-convex, existing solutions normally rely on successive convex approximation (SCA) and use off-the-shelf convex solvers, which implement an interior-point algorithm, to solve derived convex problems. The complexity of such methods scales quickly with the problem size. Therefore, we propose an accelerated projected gradient method to solve the considered problems. Particularly, each iteration of the proposed solution is given in a closed form and only requires the first order oracle of the objective, rather than the Hessian matrix as in known solutions, and thus is much more memory efficient. Numerical results demonstrate that our proposed solution achieves the same utility performance but with far less run-time, compared to the SCA method. Simulation results show that large-scale cell-free massive MIMO has the intrinsic user fairness, i.e. the four utility functions can deliver nearly uniformed services to all users.

Millimeter Wave Massive MIMO Downlink Per-Group Communications With Hybrid Linear Precoding

We address the problem of analyzing and classifying into groups the downlink channel environment in a dense millimeter-wavelength cell, accounting for path loss, multipath fading, and User Equipment (UE) blocking, by employing a hybrid propagation and multipath fading model, thus using accurate inter-group interference modeling. The base station (BS) employs a large Uniform Planar Array (UPA) to facilitate massive Multiple-Input, Multiple-Output (MIMO) communications with high efficiency. UEs are equipped with a single antenna and are distributed uniformly within the cell. The key problem is analyzing and defining groups toward efficient precoding. Because balanced throughput is desired between groups, up to four separate frequency sub-carriers are employed in an Orthogonal Frequency Division Multiple Access (OFDMA) system. We show that by employing three or four OFDMA subcarriers, depending on the number of UEs in the cell and the cell range, the UEs can be efficiently separated into <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">high-throughput</i> groups, with each group employing Virtual Channel Model Beams (VCMB) based inner precoding, followed by efficient Multi-User Multiple-Input Multiple-Output (MU-MIMO) outer precoders. For each group, we study two different sub-grouping methods offering different advantages. We show that the improvement offered by Zero-Forcing Per-Group Precoding (ZF-PGP) over Matched Filter Precoding (MFP) and Zero-Forcing Precoding (ZFP) is very high when finite-alphabet inputs are used. We also show ZF-PGP with finite-alphabet inputs significantly outperforms MFP with Gaussian inputs in certain realistic setups. Finally, a new technique for power allocation among different UEs is proposed, called Optimized Per-Group Power Allocation (OPGPA), which achieves much higher power efficiency jointly with equal throughput among all UEs in each group.

Deep learning based user grouping for FD-MIMO systems exploiting statistical channel state information

The joint spatial division and multiplexing (JSDM) is a two-phase precoding scheme for massive multiple-input-multiple-output (MIMO) system under frequency division duplex (FDD) mode to reduce the amount of channel state information (CSI) feedback. To apply this scheme, users need to be partitioned into groups so that users in the same group have similar channel covariance eigenvectors while users in different groups have almost orthogonal eigenvectors. In this paper, taking the clustered user model into account, we consider the user grouping of JSDM for the downlink massive MIMO system with uniform planar antenna array (UPA) at base station (BS). A deep learning based user grouping algorithm is proposed to improve the efficiency of the user grouping process. The proposed grouping algorithm transfers the statistical CSI of all users into a picture, and utilizes the deep learning enabled objective detection model you look only once (YOLO) to divide the users into different groups rapidly. Simulation results show that the proposed user grouping scheme can achieve higher sum rate with less time delay.

Joint Antenna and User Scheduling in the Massive MIMO System Over Time-Varying Fading Channels

Massive multiple-input multiple-output (MIMO) technology, mainly equipped with dozens or even hundreds of antennas at transmitter and/or receiver, is one of the most important technologies in 5G/6G era due to its capability of achieving high transmission rate. However, since each transmit antenna typically needs a complete radio frequency (RF) chain, a large number of RF chains need to be installed accordingly, resulting in high economic cost, high hardware complexity, and high power consumption. To resolve these problems, architectures where a small number of RF chains are installed have been proposed in recent years, and an antenna selection technique that activates antennas only as many as the number of RF chains has been envisioned as one of solutions. In this paper, we study the joint antenna and user scheduling problem for the downlink massive MIMO system over time-varying fading channels to maximize the weighted average sum rate while ensuring users’ minimum average data rate requirements. To solve the problem, we first develop an opportunistic joint antenna and user scheduling algorithm (OJAUS) using the dual and stochastic subgradient methods, which makes it possible to schedule antennas and users without any underlying distributions of the fading channels. However, it requires solving a joint antenna and user selection (JAUS) problem to maximize the instantaneous weighted sum rate in every time slot. Thus, we additionally develop a simple heuristic JAUS algorithm with low computational complexity, called JAUS-LCC, which is executed in every time slot within OJAUS. Finally, through simulation results, we first show that our JAUS-LCC provides near-optimal performance despite requiring very low computational complexity, and then show that our OJAUS with JAUS-LCC well guarantees given minimum average data rate requirements.

Beam-Domain Anti-Jamming Transmission for Downlink Massive MIMO Systems: A Stackelberg Game Perspective

In this paper, beam-domain (BD) anti-jamming transmission in a downlink massive multiple-input multiple-output (MIMO) system is investigated. A smart jammer with multiple antennas attempts to interfere with the signal reception of users with the desired energy efficiency (EE), whereas a base station (BS) tries to minimize the transmission cost while ensuring uninterrupted communication. A Bayesian Stackelberg game between the BS and jammer, where the jammer is the follower and the BS acts as the leader, is modeled. In the follower subgame, the optimal jamming precoding with a closed-form power solution is introduced. The optimal jamming power is proportional to the transmission power in the downlink, and thus, for the BS, the strategy of suppressing malicious attacks by increasing the transmission power fails. In the leader subgame, generalized zero-forcing (ZF), whose closed-form power solution constitutes the unique Stackelberg equilibrium (SE) with that of the jammer, is found to be the optimal anti-jamming precoding for robust transmission. The results show that there always exists a precoding solution for the BS that ensures reliable transmission when the SE is obtained. A proper increase in the minimum signal-to-interference-and-noise ratio (SINR) threshold or the BD channel approximation error helps the BS save power during the resistance against the jammer. Then, a simplified power solution without the instantaneous channel state information (CSI) of jamming channels is further introduced for practical implementation. Numerical results are provided to verify the proposed solutions.

An Efficient Estimation of the Number of Optimal Iterations for GS Pre-coding in Downlink Massive MIMO Systems

This paper proposes an estimation scheme of the number iterations for optimal Gauss–Seidel (GS) pre-coding in the downlink massive multiple input multiple output (MIMO) systems for the first time. The number of iterations in GS pre-coding is one of the key parameters and should be estimated accurately prior to signal transmission in the downlink systems. For efficient estimation without presentations of the closed-form solution for the GS pre-coding symbols, the proposed estimation scheme uses the relative method which calculates the normalized Euclidean distance (NED) between consecutive GS solutions by using the property of the monotonic decrease function of the GS solutions. Additionally, an efficient initial solution for the GS pre-coding is proposed as a two term Neumann series (NS) based on the stair matrix for improving the accuracy of estimation and accelerating the convergence rate of the GS solution. The evaluated estimation performances verify high accuracy in the downlink massive MIMO systems even in low loading factors. In addition, an additional complexity for estimating the number of the optimal iterations is nearly negligible.

Max-Min Power Control in Downlink Massive MIMO With Distributed Antenna Arrays

In this paper, we investigate optimal downlink power allocation in massive multiple-input multiple-output (MIMO) networks with distributed antenna arrays (DAAs) under correlated and uncorrelated channel fading. In DAA massive MIMO, the base station (BS) consists of multiple antenna sub-arrays. Notably, the antenna sub-arrays are deployed in arbitrary locations within a DAA massive MIMO cell. Consequently, the distance-dependent large-scale propagation coefficients are different from a user to these different antenna sub-arrays, which makes power control a challenging problem. We assume that the network operates in time-division duplex mode, where each BS obtains the channel estimates via uplink pilots. Based on the channel estimates, the BSs perform maximum-ratio transmission in the downlink. We then derive a closed-form signal-to-interference-plus-noise ratio (SINR) expression, where the channels are subject to correlated fading. Based on the SINR expression, we propose a networkwide max-min power control algorithm to ensure that each user in the network receives a uniform quality of service. Numerical results demonstrate the performance advantages offered by DAA massive MIMO. For some specific scenarios, DAA massive MIMO can improve the average per-user throughput up to 55%. Furthermore, we demonstrate that channel fading covariance is an important factor in determining the performance of DAA massive MIMO.

Network Massive MIMO Transmission Over Millimeter-Wave and Terahertz Bands: Mobility Enhancement and Blockage Mitigation

Mobility and blockage are two critical challenges in wireless transmission over millimeter-wave (mmWave) and Terahertz (THz) bands. In this paper, we investigate network massive multiple-input multiple-output (MIMO) transmission for mmWave/THz downlink in the presence of mobility and blockage. Considering the mmWave/THz propagation characteristics, we first propose to apply per-beam synchronization for network massive MIMO to mitigate the channel Doppler and delay dispersion effects. Accordingly, we establish a transmission model. We then investigate network massive MIMO downlink transmission strategies with only the statistical channel state information (CSI) available at the base stations (BSs), formulating the strategy design problem as an optimization problem to maximize the network sum-rate. We show that the beam domain is favorable to perform transmission, and demonstrate that BSs can work individually when sending signals to user terminals. Based on these insights, the network massive MIMO precoding design is reduced to a network sum-rate maximization problem with respect to beam domain power allocation. By exploiting the sequential optimization method and random matrix theory, an iterative algorithm with guaranteed convergence performance is further proposed for beam domain power allocation. Numerical results reveal that the proposed network massive MIMO transmission approach with the statistical CSI can effectively alleviate the blockage effects and provide mobility enhancement over mmWave and THz bands.

Uplink-Aided High Mobility Downlink Channel Estimation Over Massive MIMO-OTFS System

Although it is often used in the orthogonal frequency division multiplexing (OFDM) systems, application of massive multiple-input multiple-output (MIMO) over the orthogonal time frequency space (OTFS) modulation could suffer from enormous training overhead in high mobility scenarios. In this paper, we propose one uplink-aided high mobility downlink channel estimation scheme for the massive MIMO-OTFS networks. Specifically, we firstly formulate the time domain massive MIMO-OTFS signal model along the uplink and adopt the expectation maximization based variational Bayesian (EM-VB) framework to recover the uplink channel parameters including the angle, the delay, the Doppler frequency, and the channel gain for each physical scattering path. Correspondingly, with the help of the fast Bayesian inference, one low complex approach is constructed to overcome the bottleneck of the EM-VB. Then, we fully exploit the angle, delay and Doppler reciprocity between the uplink and the downlink and reconstruct the angles, the delays, and the Doppler frequencies for the downlink massive channels at the base station. Furthermore, we examine the downlink massive MIMO channel estimation over the delay-Doppler-angle domain. The channel dispersion of the OTFS over the delay-Doppler domain is carefully analyzed and is utilized to associate one given path with one specific delay-Doppler grid if different paths of any user have distinguished delay-Doppler signatures. Moreover, when all the paths of any user could be perfectly separated over the angle domain, we design the effective path scheduling algorithm to map different users' data into the orthogonal delay-Doppler-angle domain resource and achieve the parallel and low complex downlink 3D channel estimation. For the general case, we adopt the least square estimator with reduced dimension to capture the downlink delay-Doppler-angle channels. Various numerical examples are presented to confirm the validity and robustness of the proposed scheme.

Energy Efficiency Optimization for Downlink Massive MIMO With Statistical CSIT

We investigate energy efficiency (EE) optimization for single-cell massive multiple-input multiple-output (MIMO) downlink transmission with only statistical channel state information (CSI) available at the base station. We first show that beam domain transmission is favorable for energy efficiency in the massive MIMO downlink, by deriving a closed-form solution for the eigenvectors of the optimal transmit covariance matrix. With this conclusion, the EE optimization problem is reduced to a real-valued power allocation problem, which is much easier to tackle than the original large-dimensional complex matrix-valued precoding design problem. We further propose an iterative water-filling-structured beam domain power allocation algorithm with low complexity and guaranteed convergence, exploiting the techniques from sequential optimization, fractional optimization, and random matrix theory. Numerical results demonstrate the near-optimal performance of our proposed statistical CSI aided EE optimization approach.

Spectral Efficiency and Energy Efficiency Tradeoff in Massive MIMO Downlink Transmission With Statistical CSIT

As a key technology for future wireless networks, massive multiple-input multiple-output (MIMO) can significantly improve the energy efficiency (EE) and spectral efficiency (SE), and the performance is highly dependant on the degree of the available channel state information (CSI). While most existing works on massive MIMO focused on the case where the instantaneous CSI at the transmitter (CSIT) is available, it is usually not an easy task to obtain precise instantaneous CSIT. In this paper, we investigate EE-SE tradeoff in single-cell massive MIMO downlink transmission with statistical CSIT. To this end, we aim to optimize the system resource efficiency (RE), which is capable of striking an EE-SE balance. We first figure out a closed-form solution for the eigenvectors of the optimal transmit covariance matrices of different user terminals, which indicates that beam domain is in favor of performing RE optimal transmission in massive MIMO downlink. Based on this insight, the RE optimization precoding design is reduced to a real-valued power allocation problem. Exploiting the techniques of sequential optimization and random matrix theory, we further propose a low-complexity suboptimal two-layer water-filling-structured power allocation algorithm. Numerical results illustrate the effectiveness and near-optimal performance of the proposed statistical CSI aided RE optimization approach.